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NCERT Class XI Mathematics - Introduction to Three Dimensional Geometry - Solutions

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Question : 19
Total: 20
A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10). Find the coordinates of the point R.
[Hint: Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by (
8k+2
k+1
,
−3
k+1
,
10k+4
k+1
)]
Solution:  
Let R(4, y, z) be any point which divides the join of P(2, –3, 4) and Q(8, 0, 10) in the ratio k : 1 internally.
∴ Coordinates of R are (
8k+2
k+1
,
−3
k+1
,
10k+4
k+1
)
But x- coordinate of R is 4
∴
8k+2
k+1
 = 4
⇒ 8k + 2 = 4k + 4 ⇒ k =
1
2
∴ y =
−3
1
2
+1
 =
−3
3
2
 = - 2
z =
10×1
2
+4
1
2
+1
 =
9
3
2
 = 6
Thus coordinates of R are (4, – 2, 6).
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